Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class First {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        //int a = 1;
        int t;
        //t = in.nextInt();
        t = 1;
        while (t > 0) {
            //out.print("Case #"+(a++)+": ");
            solver.call(in,out);
            t--;
        }
        out.close();

    }

    static class TaskA {
        public void call(InputReader in, PrintWriter out) {
            int a, b, k;
            a = in.nextInt();
            b = in.nextInt();
            k = in.nextInt();

            if(a==0 || b==1){
                if(k!=0){
                    out.println("No");
                }
                else{
                    out.println("Yes");
                    if(a==0){
                        for (int i = 0; i < a+b; i++) {
                            out.print("1");
                        }
                        out.println();
                        for (int i = 0; i < a+b; i++) {
                            out.print("1");
                        }
                    }
                    else{
                        out.print(1);
                        for (int i = 1; i < a+b; i++) {
                            out.print("0");
                        }
                        out.println();
                        out.print(1);
                        for (int i = 1; i < a+b; i++) {
                            out.print("0");
                        }
                    }
                    out.println();
                }
                return;
            }
            if(k>a+b-2){
                out.println("No");
                return;
            }
            if(k==0){
                out.println("Yes");
                for (int i = 0; i < b; i++) {
                    out.print("1");
                }
                for (int i = b; i < a+b; i++) {
                    out.print("0");
                }
                out.println();

                for (int i = 0; i < b; i++) {
                    out.print("1");
                }
                for (int i = b; i < a+b; i++) {
                    out.print("0");
                }
                out.println();
                return;
            }

            out.println("Yes");
            StringBuilder s1 = new StringBuilder("1");
            StringBuilder s2 = new StringBuilder("1");
            b--;
            int n = a+b, c , d;
            c = n - 1 -k;

            for (int i = 0; i < c; i++) {
                if(b==1){
                    s1.append("0");
                    s2.append("0");
                }
                else {
                    s1.append("1");
                    s2.append("1");
                    b--;
                }
            }
            s1.append("1");
            s2.append("0");
            d = b;
            b--;

            for (int i = c+1; i < n; i++) {
                if(b!=0){
                    s1.append("1");
                    b--;
                }
                else {
                    s1.append("0");
                }
            }

            b = d;
            for (int i = c+1; i < n-1; i++) {
                if(b!=1){
                    s2.append("1");
                    b--;
                }
                else {
                    s2.append("0");
                }
            }
            s2.append("1");

            out.println(s1);
            out.println(s2);

        }
    }

    static int gcd(int a, int b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }

    static class answer implements Comparable<answer>{
        int a;
        int b;

        public answer(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(answer o) {
            return o.a - this.a;
        }

        @Override
        public boolean equals(Object o){
            if(o instanceof answer){
                answer c = (answer)o;
                return a == c.a && b == c.b;
            }
            return false;
        }
    }

    static class answer1 implements Comparable<answer1>{
        int a, b, c;

        public answer1(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;

        }

        @Override
        public int compareTo(answer1 o) {
            if(o.c==this.c){
                return this.a - o.a;
            }
            return o.c - this.c;
        }
    }

    static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static void sort(long[] a) {
        ArrayList<Long> l=new ArrayList<>();
        for (long i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static final Random random=new Random();

    static void shuffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}